In my personal experience the difference between the "um zu" and the "zum" is not as important as the position within the sentence.
If the "reason" is not located directly after the noun ("Platz") the "reason" refers to the whole sentence:
Wir müssen einen besseren Platz finden, um Fußball zu spielen.
Zum Fußballspielen müssen wir einen besseren Platz finden.
I'm not 100% sure about the official "Hochdeutsch" but in the dialect I speak both sentences have absolutely the same meaning:
The construction explains why something is or has to be done: Another place has to be found because you want to play football.
When the "zum" construction however is placed directly after the noun the meaning changes:
Wir müssen einen besseren Platz zum Fußballspielen finden.
In this case the construction "zum Fußballspielen" does not refer to the whole sentence but to the noun ("Platz"): It describes what kind of place has to be found. It does not (explicitly) give a reason why such a place must be found.
In the dialect spoken here I sometimes heared constructions like these:
Wir müssen einen besseren Platz, um Fußball zu spielen, finden.
Wir müssen einen besseren Platz finden zum Fußballspielen.
I'm not sure if these constructions are allowed in "official" German (and if yes: if the commas are correct) or if they are only used in dialect.
In the first case the "um Fußball zu spielen" is placed directly after the nown. Therefore it is a description of the place.
In the second case the "zum Fußball spielen" is not placed directly after the noun but the word "finden" is separating the noun from the construction. Therefore the construction refers to the whole sentence.
Theoretically you may even combine both cases - however most Germans would use "um zu" in this case because using "zum" twice in one sentence sounds wrong:
Zum Toreschießen müssen wir einen besseren Platz zum Fußballspielen finden.