I can speak to this question as I had 2001 Tundra and now have a 2011 SR5. In between I drove a WRX and Legacy GT, so I guess you could say I enjoy performance driving to some degree.
I know exactly what you are talking about with the solid and confident feel of the Tundra, which I think was attributable to its relatively wide stance and lowish center of gravity and seating position. Being a truck, of course, it could lose its back end in the corners, but it was a fine canyon carver and wonderful on the highway. However, I never enjoyed driving it in the city as it felt unresponsive (I almost always drove in 2nd gear just to have enough response from the automatic transmission in traffic), and too big to maneuver around very well. Also, the V-8, which I loved, wasn't really all that fast (particularly at altitude and we live in Tahoe at the time) - It just sounded that way with the TRD exhaust.
The SR5 reminds me of the short drive I took in a 4-door Tacoma before deciding to move from the WRX to the Legacy. It feels higher and bouncier than the Tundra, which can be a little off-putting initially. It also seems more prone to drift on the highway and is more sensitive to correction - All of which I think is related to width/length/height dynamics. However, after changing the tires to Revo2s (see other thread), I have been exploring the driving characteristics a little more and I've been pleasantly surprised.
Not that this would be important to everybody, but I have to back out of my driveway with some tight and nimble turning and I find that the SR5 does this as well or better than my previous sedan, which speaks to the fine city driving that comes with this truck. You can really move this vehicle around town nicely as it has great visibility, tight cornering, and good steering response at low speeds. Also, the sport shift mode gives better options for engaged driving than simply putting the column shift in 2nd and doing your best. These same attributes will make rolling over Ebbett's Pass in the Sierras this next summer (a trip I make quite frequently) rather fun as opposed to a chore. This road climbs aggressively and swaps between super-tight hairpins and short straight stretches and I think the SR5 will eat this up almost as well as my previous sedans (except for the acceleration out of the turns, of course).
Another revelation is the cornering. Yes, it has a high center of gravity, but I was amazed that a long, rolling onramp I travel daily provided me with about the same exit speed in the SR5 as with the Legacy. Frankly, I was shocked as I fully expected to be leaning and fighting this turn and instead, with the whole family inside, we cruised along without any exclamations of fear (or joy) from the passengers. There's more engineering at play in the suspension of this vehicle than its deterrents in the various reviewing organizations acknowledge when they quickly determine that the 4Runner "drives like a truck." This attribute makes quick runs with on-a-dime turns through intersections with changing lights something you can pull off without fearing that you'll be rolling over the curb as the light turns red, which means it can handle multiple roles in your household, I think.
The SR5 reminds me most of a truck I loved years ago. I had the 1st gen Tacoma (circa '95) in a regular cab, V6, and 5-speed transmission. This car was a rocket and so fun to drive, but it went to a whole different level when I put a steel shell (as opposed to the lighter fiberglass type) on the back. Once the weight was better balanced this truck ran on rails and I called it, at the time, the best sports car I ever owned. I think the weight balance of the 4Runner helps in the same way and the overall weight, which is heavy to be sure, does help keep the vehicle on the road, even if it creates other less advantageous attributes as well.
All said, everything is a compromise in some ways. I do lament that you can't really buy the old Tundra anymore as there is nothing quite like it in current production. But, there is a bit of unacknowledged magic in the engineering of the current 4Runner, even without X-REAS or KDSS, that makes it an on-going revelation (I've only had it a couple of weeks or so). Lastly, I think your question is pertinent as my first drive with the salesperson in tow hardly revealed the things I'm speaking of now. I was mildly impressed and generally excited that I could satisfy our family’s need for a vehicle with a third row and still get something that could be fun, manly, and cool. First impressions, however, are not the full story on this vehicle, which is why, I think, lots of reviewers tend to get it wrong in some ways.
Really, what this vehicle needs to be great is simply more power or, at least, power delivered better. While I would love to have a TRD charger on this engine, all it really needs is a Cobb reflash of the ECU to change the preset shift points to align more closely with the power curve and open it up a little more and it would be much better in every driving situation. Of course, that'll hurt gas mileage, so we got what we got.
By the way, I'm pretty sure I'm going forward with the K&N 63 Series and Borla Cat-back paired install pretty soon to try and open up the system and create the kind of throttle response that helps make up for some of the bottled-up driving dynamics inherent in the engine/tranny combo. Watch my other thread for details.
Good luck!
DP