Wee all the way!
Get the Wee.
First the Wee is NOT slow. Sure an SV650 is quicker, but not much. It covers the 1/4 mile in 12.5 seconds which is barely 2/10 of a second second slower than the F800GS or Tiger 800. For reference in the mid-eighties an RZ350 ran a 13.5 second 1/4 mile and was considered a crazy fast hooligan bike with its twin cylinder 350cc 2-stroke motor. My 2004 VFR ran a 11.25 second 1/4 mile and did not feel that much quicker to me unless above 9000 RPMs. Finally, few street cars other than exotics and pure muscle cars can do under a 14 second 1/4 mile in stock trim, which either bike can beat ... easily.
The Wee is reliable. Sure it will wear out bearings, shocks, and tires like any bike. But electrical systems, engine, transmission, and basic hardware are extremely reliable in my experience as good as any Japanese bike I've owned. Consequently, you can rev it all day without fear of a break down or a speeding ticket.
A piped Wee will sound good.
A stock Tiger will sound good.
Both good choices, but do not dismiss a modern 650cc twin just because by today's high standards it's spec sheet does not seem very impressive!
'12 DL650 Adventure; '08 KTM 990 Adv w/19" front Excel; '09 Sherco ST 2.9 trials; '03 KLX400SR