a single classed pathfinder character is probably more powerful than a single classed 3.5 character (with the disclaimer that there was enough stuff released for 3.5 that you could make severely broken characters with the right selection of spells and feats)
If you do an apples-to-apples comparison (compare the 3.5 class to PF version) the PF version of any core character is definitely more powerful. Broken and 3pp characters may deviate from this.
I was told PF characters are about the equivalent of 3.5 characters of a level higher. So a level 5 PF rogue is about as powerful as a level 6 3.5 rogue. I suspect this may be underestimating PF characters and the disparity may even be greater at higher levels (a level 15 PF rogue may be equal to a level 17 or 18 3.5 rogue).
Also IIRC a PF CR is designed for a group of four PF PCs, where a 3.5 CR is designed for 5 3.5 PCs. I think a PF CR is one lower than a 3.5 CR, so a 5 PF CR designed for four level 5 PF characters is equal to a 6 3.5 CR designed for five level 6 3.5 characters.
Every class gets something every level in PF - there are no dead levels. All characters get a feat every odd level. Many classes get a type of class feat - a rogue talent, a barbarian rage power, etc., every even level. Unlike 3.5 many classes essentially get a feat every level. Classes that don't get a feat every level usually get something of approximately equal power. 3.5 characters get significantly less goodies. Feats also get bumped. For example dodge now grants a +1 dodge bonus to all enemies, whereas previously you had to designate one enemy to dodge. Toughness now gives +3 hp and +1 hp every level after 3, rather than a flat +3 bonus.
As has been the trend since 1E every edition change (1 to 2 to 3 to PF/4) bumps the power level of characters. Characters are increasingly defined by the benefits they pick, rather than penalties incurred in exchange for picking strengths. For example racial modifiers are now +2, +2, -2 rather than +2, -2. Characters get more feats. Characters have incentives to single-class and pick class-skills where they were previously penalized for multi-classing and picking cross-class skills. Increasingly penalties and drawbacks for making choices your character would not naturally excel at are replaced by rewards for build choices your character would excel at. Numbers inflate all-around.
I don't believe 3.5 classes, prestige classes, and possibly feats and races can be integrated into a PF game without serious revamping and a near-professional understanding of how game balance works in both games. Modules are fine, but I'd bump up the power of monsters arbitrarily if the game feels to easy.
4E takes this trend even further and the numbers are on such a different level that, unlike PF, the games are not even remotely compatible. The philosophy of both games is to make PCs (and consequently monsters) stronger and defined by the strengths they choose. The drawback is numbers rapidly inflate, new gamers are frequently overwhelmed by choices and powers and newer games are characterized by increasingly complex PCs. If you want to go in the other direction and dial-back numbers and complexity I'd suggest Castles and Crusades, AD&D or Old-School Renaissance products. Contrary to what you'd expect these games tend to play faster and simpler with much less rules while offering dramatically fewer choices for character customization.
I may have gotten some very specific facts wrong but the jist is essentially true.