It does IMO. Being the top team in the city should mean a lot. When we had the Bonetti side (For all its flaws) most of the bairns in town were kicking about in Dundee tops, now I appreciate a lot of that was also down to big name signings but a lot of it was attributed to us being top dogs in the city - this all happened very quickly. We pushed how great our youth setup was becoming - what happened to it? Are the best players in town really still coming to dens?
I haven't seen the finances of both clubs, but I'd be pretty confident that our budget is higher than United's. I'd also suggest being in a higher league does directly influence budget and attracting players. Have we used that budget wisely?