Here is a comparison based on my testing with a tome warlock.  First a chart for the pact magic vs caster progression table:
| Level | 0 SR | 1 SR | 2 SR | 3 SR | UA Progression | 5e Arcanum | UA Arcanum | 
| 1 | 1 | 2 | 3 | 4 | 2 | 0 | 0 | 
| 2 | 2 | 4 | 6 | 8 | 2 | 0 | 0 | 
| 3 | 2 | 4 | 6 | 8 | 3 | 0 | 0 | 
| 4 | 2 | 4 | 6 | 8 | 3 | 0 | 0 | 
| 5 | 2 | 4 | 6 | 8 | 6 | 0 | 0-2 | 
| 6 | 2 | 4 | 6 | 8 | 6 | 0 | 0-3 | 
| 7 | 2 | 4 | 6 | 8 | 7 | 0 | 0-4 | 
| 8 | 2 | 4 | 6 | 8 | 7 | 0 | 0-4 | 
| 9 | 2 | 4 | 6 | 8 | 9 | 0 | 0-5 | 
| 10 | 2 | 4 | 6 | 8 | 9 | 0 | 0-5 | 
| 11 | 3 | 6 | 9 | 12 | 10 | 1 | 0-6 | 
| 12 | 3 | 6 | 9 | 12 | 10 | 1 | 0-6 | 
| 13 | 3 | 6 | 9 | 12 | 11 | 2 | 0-7 | 
| 14 | 3 | 6 | 9 | 12 | 11 | 2 | 0-7 | 
| 15 | 3 | 6 | 9 | 12 | 12 | 3 | 0-8 | 
| 16 | 3 | 6 | 9 | 12 | 12 | 3 | 0-8 | 
| 17 | 4 | 8 | 12 | 16 | 14 | 4 | 0-9 | 
| 18 | 4 | 8 | 12 | 16 | 14 | 4 | 0-9 | 
| 19 | 4 | 8 | 12 | 16 | 15 | 4 | 0-9 | 
| 20 | 4 | 8 | 12 | 16 | 15 | 4 | 0-9 | 
 
Note that at 5th level the option exists to take 
mystic arcanum and to swap out a previous invocation for another 
mystical arcanum of a different level, and at 6th level the other invocation preceding 5th level can also be swapped out for a 
mystic arcanum.  I wouldn't do this because I prefer at-will invocations but the chart notes that it's possible to spend all invocations on 
mystic arcanum.
Other than low levels, the actual number of spell actions between the two isn't heavily in favor of the standard assumption.  Only the spell levels are the significant concern.  And it is a fair point that it's a significant concern. 
I went vanilla with a human.  The default gave me 
resourceful, 
skillful, and 
versatile.
I went cultist for the background.  That gave me +2 INT, +1 CHA, arcana proficiency, religion proficiency, disguise kit proficiency, 
magic initiate.
I usually use point buy, but standard array is more typical of rolling method or array so went that route for playtesting.  I know I could manage the ability scores better but I choose my perception of the character over eeking out advantages.  ;-)
STR:  8
DEX:  13
CON:  12
INT:  14+2=16
WIS:  10
CHA:  15+1=16
So the first level is rather extremely different.  Giving up the short rest recharge gave me 3 cantrips instead of 2 based on the class because 
Eldritch Blast and 
Hex are free for all warlocks as bonus spells now.  I went tomelock (INT), which gave me 
book of shadows immediately so at 1st level...
warlock cantrips: eldritch blast, prestidigition, minor illusion
magic initiate (arcane) cantrips: mage hand, mending
book of shadows cantrips: guidance, resistance
warlock spells:  hex, shield, sleep
magic initiate (arcane) spell: thunderwave
book of shadows spells: find familiar, detect magic
Gaining the pact ability at 1st level instead of 3rd level makes a big difference for the class.  A background feat isn't part of the class but it also clearly makes a big difference to the overall character.  I was not struggling with using magic at 1st level. 
skill proficiencies:  arcana, religion, persuasion (skillful), history (skilled), deception (skilled), insight (skilled)
armor training: light, medium
At 2nd level I picked up 
armor of agathys for a prepared spell, 
misty visions (invocation), and 
agonizing blast (invocation).  The number of cantrips available and free casting of 
silent image at will continues to make a caster warlock doable.
At 3rd level I grabbed 
alarm because the ritual caster feature is no longer necessary.  This also granted me 
burning hands and 
command. 
At 4th level INT bumped to 18 with the ability score feat, and I added 
identify and 
message.
At 5th level I swapped out 
sleep for
 levitate and added 
darkness.  I replaced 
agonizing blast invocation with 
devil's sight because the book of shadows upgrades damage enough at that point, and I added 
fireball via 
mystic arcanum.  The patron features added 
suggestion and 
scorching ray.
6th level was the subclass feature and not part of the spells specifically but 
dark one's own luck is useful.  At 7th level I added 
detect thoughts, and 
wall of fire via 
mystic arcanum.
8th level was the ability increase feat to change INT to 20 and felt like a bit of a dead level.  At 9th level I added 
fear and 
stinking cloud as patron spells, 
clairvoyance and 
dispel magic via spells prepared, and 
animate objects as 
mystic arcanum.  Replaced 
alarm with 
Leomund's tiny hut.
10th level was another subclass feature.  Added the 
friends cantrip.
11th level adds 
contact other plane as a class feature.  I added 
comprehend languages for the spells prepared.  I replaced the 
fireball mystic arcanum with 
circle of death via mystic arcanum, and added 
whispers of the grave.
12th level I increased CON to 14.  At 13th level the patron spells added 
wall of fire and 
blight.  I replaced 
wall of fire from 
mystic arcanum with 
teleport.  I added 
polymorph.  I added 
gift of the protectors.
14th level adds 
hurl through hell.  At 15th level I added 
dimension door.  I added 
glibness through 
mystic arcanum. 
At 16th level I took the durable feat.  CON went up to 15 and the warlock could expend HD for healing using a bonus action.
17th level adds 
flame strike and 
insect plague as patron spells.  I added 
animate objects and 
scrying.  I replaced the 
animate objects from
  mystic arcanum with 
wish.  I added 
master of myriad forms.
At 18th level 
hex becomes at will.  I traded replaced 
teleport from 
mystic arcanum with 
forcecage.  At 19th level I added 
misty step, and bumped DEX to 14 and CON to 16. 
20th level added +2 INT and 
epic boon of the night spirit.  We played around with epic and I later added 
epic boon of energy resistance.
Build at the end of playing was:
AC 19 (+3 breastplate)
163 hp
STR: 8 (saves -1)
DEX: 14 (saves +2)
CON: 16 (saves +3)
INT: 24 (saves +7)
WIS: 10 (saves +6)
CHA: 16 (saves +9)
athletics (-1); acrobatics (+2), sleight-of-hand (+2), (stealth +2); arcana (+13), history (+13), investigation (+7), nature (+7), religion (+13); animal handling (+0), insight (+6), medicine (+0), perception (+0), survival (+0); deception (+9), intimidation (+3), performance (+3), persuasion (+9)
cantrips: 
eldritch blast, prestidigitation, minor illusion, mage hand, mending, guidance, resistance, message, friends
1st-level -- 
hex, shield, thunderwave, find familiar, detect magic, armor of agathys, burning hands, command, Identify, comprehend languages
2nd-level -- 
suggestion, scorching ray, darkness, levitate, detect thoughts, misty step
3rd-level -- 
fear, stinking cloud, clairvoyance, dispel magic, leomund's tiny hut
4th-level -- 
wall of fire, blight, polymorph, dimension door, hurl through hell
5th-level -- 
contact other plane, flame strike, insect plague, animate objects, scrying
6th-level -- 
circle of death
7th-level -- 
forcecage
8th-level -- 
glibness
9th-level -- 
wish
Invocations: 
mystic arcanum (x4), 
misty visions, 
devil's sight, 
whispers of the grave, 
gift of the protectors, 
master of myriad forms
There is a free casting of 
thunderwave, 
hurl through hell, 
contact other plane, and one of the patron spells.  The following spells can be cast at will: 
hex, 
silent image, 
alter self, 
speak with dead.  The following spells can be cast as rituals: 
find familiar, 
detect magic, 
identify, 
comprehend languages, 
leomund's tiny hut, 
contact other plane.
Medium armor was added, 
dark one's own luck increased uses, and
 fiendish resilience is fairly flexible.  Access to spells like 
shield helps now and I'll point out that 
absorb elements seem to have been removed from the arcane spell list.  With epic boons, 
epic boon of the night spirit granted resistance to all damage types other than force, psychic, and radiant with some darkness.  
Epic boon of resistance added resistance to psychic and radiant.
Find familiar was a bit disappointing.  Now that the familiar from the arcane list spell is based on spell level warlocks using the spell have a worse familiar.  
Wish, OTOH, can still replicate any spell of 8th level or lower, which becomes problematic when creating class only spells.  I could use 
wish to cast the 
pact familiar cantrip.
A sorcerer can use wish to grab 
book of shadows and 
pact familiar.  And all kinds of shenanigans during downtime by being immune to losing 
wish forever.
I did not feel weaker in low levels.  I do think shared spell lists look like more trouble than they're worth.