Playing with a chainlock to check out the difference. The choices I made were similar to the tomelock I tried.
Vanilla with a human. The default gave me resourceful, skillful, and versatile. This time I replaced versatile with magic initiate (divine).
Cultist for the background again. That gave me +2 INT, +1 CHA, arcana proficiency, religion proficiency, disguise kit proficiency, magic initiate (arcane).
Standard array again. I also chose INT for the caster stat again for concept reasons.
STR: 8
DEX: 13
CON: 12
INT: 14+2=16
WIS: 10
CHA: 15+1=16
No book of shadows immediately so at 1st level this time...
warlock cantrips: eldritch blast, prestidigition, minor illusion
magic initiate (arcane) cantrips: mage hand, mending
magic initiate (divine) cantrips: guidance, resistance
warlock spells: hex, shield, sleep
magic initiate (arcane) spell: thunderwave
magic initiate (divine) spell: detect magic
The familiar at 1st level instead of 3rd level is still better, and stat increases based on warlock level instead of spell level to create it works better than using the standard arcane spell.
skill proficiencies: arcana, religion, insight (skillful), history, investigation
armor training: light, medium
Very little changed as I leveled up. I had 3 less skill proficiencies but still had plenty of cantrips and a better familiar. My familiar was a floating undead skull named Bob.
At 2nd level 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 alarm, burning hands, and command again.
At 4th level INT to 18, identify, and message again.
At 5th level I swapped out sleep for levitate and added alter self this time. I kept agonizing blast invocation without the book of shadows damage upgrade, and I added animate dead via mystic arcanum. Plus suggestion and scorching ray.
Without the free bonus damage I felt obligated to keep agonizing blast and I felt like I was one invocation behind moving forward because of it compared to the tomelock. I didn't need investment of the chain master or voice of the chain master, and the floating familiar that could use it's actions to remain invisible was useful, and I was more inclined to use the familiar for additional combat support with the changes; but it still felt like I needed agonizing blast due to the prevalence of damage in combat.
6th level dark one's own luck is still useful. At 7th level I added detect thoughts, and blight via mystic arcanum.
8th level was INT to 20 again. 9th level fear and stinking cloud as patron spells, animate dead and dispel magic via spells prepared, and scrying as mystic arcanum. Replaced alarm with Leomund's tiny hut. Replaced animate dead mystic arcanum with favor of the chainmaster.
10th level added friends cantrip.
11th level I added comprehend languages and I replaced the blight 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 added polymorph. I added teleport through mystic arcanum.
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 modify memory and scrying. I replaced the scrying from mystic arcanum with wish. I added master of myriad forms. I replaced alter self with darkvision.
I used wish to add a book of shadows for thaumaturgy and druidcraft cantrips, and added tensers floating disk and unseen servant rituals.
At 18th level I replaced the agonizing blast invocation with devil's sight because of the bonus from book of shadows, and replaced darkvision with darkness.
At 19th level I added misty step, and bumped DEX to 14 and CON to 16. I replaced teleport with forcecage.
20th level added +2 INT and epic boon of the night spirit. I added epic boon of fate instead.
Build at the end of playing was:
AC 18 (+2 breastplate)
163 hp
STR: 8 (saves -1)
DEX: 14 (saves +2)
CON: 16 (saves +3)
INT: 22 (saves +6)
WIS: 10 (saves +6)
CHA: 16 (saves +9)
athletics (-1); acrobatics (+2), sleight-of-hand (+2), (stealth +2); arcana (+12), history (+12), investigation (+12), nature (+6), religion (+12); animal handling (+0), insight (+6), medicine (+0), perception (+0), survival (+0); deception (+3), intimidation (+3), performance (+3), persuasion (+3)
cantrips: eldritch blast, prestidigitation, minor illusion, mage hand, mending, guidance, resistance, message, friends, thaumaturgy, druidcraft
1st-level -- hex, shield, thunderwave, detect magic, armor of agathys, burning hands, command, Identify, comprehend languages, unseen servant, tenser's floating disk
2nd-level -- suggestion, scorching ray, darkness, levitate, detect thoughts, misty step
3rd-level -- fear, stinking cloud, animate dead, 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, modify memory, 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, favor of the chainmaster, master of myriad forms, book of shadows (added via wish)
There is a free casting of thunderwave, detect magic, 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: detect magic, identify, comprehend languages, unseen servant, tenser's floating disk, leomund's tiny hut, contact other plane.
I did feel like I was behind an invocation from 5th level on through 16th but wish corrected that. Access to spell levels is more of a pain but mystic arcanum does mitigate that. I don't see the need to level gate mystic arcanum and still think another invocation at 3rd and 19th levels makes sense but over-all the UA version does work.