Faced with almost the exact dilemma, I chose the BX and BOY am I GLAD that's how I went. I mow a little more than 1 acre of heavily wooded grass and can get it done (including bagging) in about 45 minutes (that's tractor time...not trimming and such). Perhaps I could get that down to 30 or even 20 minutes with a ZTR, but along with gaining 15 to 25 minutes of my life, I'd lose one of the best tools I've ever purchased. I do EVERYTHING with my BX and the mow quality is exceptional.
Alternately, my cousin mows 5 acres of open field every week. That's his yard. His Kubota ZD21 FLIES and gets the job done much faster than a BX would. In his case, he's much better with a ZTR and a non-mowing
B21...the exact solution he's deployed.
If you're looking for one solution, go with the BX. I hate renting things. Don't like the timetable it puts on my projects. You'll gain little time in mow speed and give up HUGE amounts of utility.
To give you an idea of how quickly a BX could dispatch 10 yards of mulch: I trailered my BX to my parents house (~3 hours away) to help fix their 1/2 acre yard. After I completely re-graded their ditchline and cut/filled numerous places in their yard (as much as 1 foot in places), I spread 6 CY of screened topsoil and 6 CY of compost blend. I evenly spread and graded that 12 CY of material in about 1 hour. I completed the entire lawn rehab job (including many, many other tasks) in 1 day. The next day, my Mom asked me to get the roots out of the back yard. Using the backhoe, I pulled ~1,000# of roots out of the ground and regraded the back yard for grass planting...that distraction took about 5 hours start to finish.
The BX is wicked-amazing.