Up through the 1920's, I think a good current club player would be able to beat most everyone, with one notable exception: Tilden. Following through into the 1930's, as per the title of the thread, I'd think Perry and Budge would have a decent shot. And that's with the technological advantage going to the modern player.
A lot would depend on which version of the rules were used. If it were an old version, requiring one foot to be kept on the ground while serving, I'd like Tilden against any club player, even with wood. Having played with wooden racquets, I can vouch that the efect they have on the serve is negligible. Philippoussis served about 2-3 MPH slower with wood than with his current stick.
One big advantage a modern player might have would be fitness. Player stamina wasn't so great in the 1920's. Old-timers make a big deal out of not having chairs during changeovers, but conveniently omit that they had 10-15 minute breaks during the matches, which allowed them to get a massage, shower, etc. And there were a lot of tanked sets back in the old days.
On the women's side, it would be hard to see the old players winning. There were two dominant players in the 1920's; Lenglen and Wills. Both had major physical deficiencies. Lenglen had no stamina, which is why she played the less demanding counterpunching style, and rarely came to net. It's also why she bombed so spectacularly in her one appearance in the US Nationals, played in the oppressive East Coast summer conditions. Wills, meanwhile, was very slow. She would make Davenport look almost like Coetzer by comparison. And her strength, her power, would be tame by today's standards.
If either of these women drew a modern player that was fit, and had fairly good control over her groundies, with the modern player having the added technological advantage, the old-timer would have no chance.