I'd rate GT4 and Enthusia equally overall, but both games have advantages and disadvantages compared to the other.
You can read my thoughts on physics here (several posts), but I came to the conclusion that EPR is better in this respect than GT4, and indeed any other PS2 game I've tried. I have to admit to not having played TXRD2 yet, but it's proving difficult to source a copy in the UK. EPR isn't perfect for physics (I find the response a bit slow-witted) but it's very good for a PS2 game.
As for the games as a whole, I like them pretty much evenly.
EPR has better physics for me, as mentioned, but GT4 wins for graphics. EPR is great and very similar to GT4, but there are a few glaring errors, such as the "unfinished" scenery that's very visible on the Dragon Range downhill course. However, the rain and wet track effects (and indeed snowy surfaces) are better in Enthusia, as are the smoke effects.
The circuits in Enthusia are more fun and more imaginative than GT4 - perhaps I'm just bored of the same old GT circuits, but tracks like the aforementioned Dragon Range, Burgenschlucht, Wintertraum and Mirage Crossing are all fantastic and miles more imaginative, whilst still looking like real places. The tracks based on real cities, like London, San Francisco and Venice, are all detailed and atmospheric. GT4 however has more real-life circuits so gains points back here.
Cars - GT4 wins for sheer numbers, and I love the inclusion of so many muscle cars and unusual vehicles, but I do like the extra variety that EPR offers. I'd welcome the inclusion into GT5 of some of the cars EPR has included - proper off-roaders, minivans, rally raid cars, the classic Morris Mini Cooper, the Smart, E30 M3, BMW 3.0 CSL, Citroen DS, MGB, Abarths, Firebird Trans Am, Saabs, more classic Japanese cars... and so on. Variety is the spice of life.
GT4 also wins for realistic tuning, but at the same time, I much prefer the ease of use of Enthusia's settings menus, and it's something that GT could definitely learn from.
So yeah, I'd say for overall realism they're about equal, on balance. As for other games, Tourist Trophy is excellent - probably better graphics and more fun than GT4, and the on-board riding view is excellent, really adds to the game just as the in-car view does in GT5P. As for rally games, I haven't played Richard Burns Rally, the Colin McRae games have great graphics and they're great fun, but the courses are too short and the handling isn't as realistic as others, and the WRC games are quite similar, maybe a little more realistic and detailed courses, but less fun.
GT3 A-Spec has better physics than GT4, in my opinion. I really felt like PD went backwards with GT4 in the physics department when compared to GT3. I've never played Enthusia so I can't compare the game but as far as games that I've played on the PS2, I'll have to say GT3.
Does anyone know where I can get a new copy of Enthusia for cheap? The only place I've found that carries the new copy is Amazon.com but they want like $42 for it.

I don't like buying used games, it has to be new because I'm anal about scratches and missing cases or manuals.
Don't be too fussy about buying used. I got my copy of Enthusia used off Amazon Marketplace for about £4, or roughly $5.70 at the current exchange rate. It's a little scuffed but nowhere near enough to even think about skipping, and the game has the full manual. Just choose buyers with lots of high feedback ratings and if they're describing it as "used - as new" you can guarantee they're telling the truth.