My girlfriend just picked up the droid x. I have the incredible. And, unlike most people on this forum who are so lost in the smugness of the pride of their phone, I like to judge things a little more objectively.
As far as "bigger" goes, yes, it's wider and it's longer than the incredible. But at it's best, it's the same thickness, if not thinner than the incredible. The incredible has all those steps that make you think it's thinner than it really is and the X does not. There's something to be said about a phone that has a (mostly) uniform cross section. It slides very easily in and out of my pocket compared to the incredible. And when I had a case on my inc, forget about it- it caught on my pocket lining ever time leading to many drops.
As far as size goes, unless you wear super tight hipster jeans, the X does just fine.
Hardware wise, I found the X to be supierior in every category. Size, screen quality, industrial design, material it's made out of, etc. It had a good weight to it, it feels superior as far as it's mechanical material goes (fees very sturdy compared to the plasticy incredible), and the screen was superior. Especially in the sun, which is very nice. Being a mechanical engineer, I appreciate the hardware side of it. The battery removal is slick and snappy, it all "clicks" together well because the clips are metallic and well designed with good snap ratios, etc. It definitely will take a drop better than the incredible just because of the material's yield strength... aluminum is exponentially better than PC/ABS and will keep energy from transfering to the glass infront of the screen. This is a very good thing for my girlfriend.
Software? That's where the incredible shined. Sense is nice. Motoblur was not up to my taste, but I'm sure with time it'd be ok. I got used to my incredible so there's a comfort factor there. I changed a bunch of the X's settings to get it "incredible like" but my girlfriend quickly scrubbed that out with her own thing on the phone. From what I could tell, the widgets on motoblur were very clunky. The social networking ones were pretty nice. But the contact widgets were pretty clunky and gaudy. And the contact list doesn't "centralize" like sense's. My contacts keeps a small neat list that I use for calling people. My girlfriend's X threw every single facebook friend of hers on her contact list and (her being a facebooker crazy girl) about had a heart attack as she's having a hard time filtering the ones she actually cares about.
Phone quality seemed the same. Call quality, sound reproduction, etc. The X seemed to have a slightly better sound reproduction. But that's about it.
Reception wise the incredible had the X hands down. She was sitting next to me on my couch, and my apartment is kind of a no-man zone for verizon. It's like the only place on earth verizon doesn't reach lol. I had to put her on my wifi network in order to get her started up on downloading apps via the market. She had good enough reception for facebook (barely) but no enough for downloading. My incredible was throttling downloads. I was getting 3g. She was getting 1x.
The X battery (out of the box) beats my stock 1350mha battery pretty bad. After I put a 1500 htc battery in it, I haven't had any issues making it through the day before hitting 40% on heavy-moderate usage. As far as how much she uses it and how long she can go without charging, it's still up in the air. But she has been making it through the day in a similar manner to my new battery. So the X has the incredible there (if the incredible is stock). But the 1500mha battery fixes this quite well for low dollar.
A lot of this is opinion, much like all the other ones on here, so take it for what you will. But a lot of this was just mere observation, too.
I was messing around with Swype last night and I'm good at it, but while holding the phone with my other hand at the same time. 
. I decided i don't need 4.3 inches and I've decided that I liked sense much better than Moto-Blur. For some reason, and again, this is just my opinion, the Inc felt snappier to me when changing menus and when texting, while the X showed early signs of chugging when flipping through pages, photos, home screens, etc. I made sure nothing was running on the X that shouldnt be, and killed all tasks to make sure nothing was clogging it up, but still i felt a slight chug when changing through home screens (doesn't the X have a faster processor). I felt the Inc was much faster in that aspect, but then again, the X's screen and color was gorgeous and while my screen is nice, i have yet to see a phone that looks better than the X. and if you even think the iPhone4 comes close to the X in terms of video quality, you're nuts (again, my opinion, and my opinion is useless). 
