Swordsman of Mars is a 1930's sword and planet story by Otis Adelbert Kline, who wrote a lot of this stuff back in the day. His ouvre was primarily based on Venus - Planet of Peril, et al - in contrast to Burroughs' John Carter of Mars novels. So why is this set on Mars...and why did Burroughs write some stories set on Venus...who knows, but the rumors of a feud between the two were probably wrong, and a little publicity never hurt anyone. There is a good introduction by Micheal Moorcock giving us a useful look at Kline, and some background. So, for all that, is Swordsman of Mars any good? Yes.
Harry Thorne, penniless and broken hearted - or rather his consciousness - is sent to Mars by way of "thought-transference" developed by an American scientist, to exchange bodies with a young Prince of Mars. This attempt at "science" may seem laughable today, but really, how he gets to Mars is as relevant as Alice going through the looking glass, except that it explains why he can't jump like he's on a trampoline, and why people think he's someone else. Its what he does once he is there that is relevant.
His mission is to track down another Earthman sent to Mars, a criminal, and to defeat a tyrannical dictator that rules with an steely fist. From this the usual adventures follow - fleeing for one's life, pretty Martian girls (in fact, Thorne finds himself in something of a love triangle; luckily - if somewhat predictably - it is two girls and him) an antogonist to be defeated, strange Martain beasts, etc - and Thorne must use all his wit and strength to avoid death and disaster. There are sieges and battles, all proceeding at a gripping pace.
Kline writes with force, and this is as good as Burroughs' tales of Mars, if set in a distinctly different world. There is nothing "new" here, in one sense, but simply a story well told to sweep along the reader.