This is a classic question and has been asked/well-addressed several times in this forum in prior answers. Suffice it to say, a $K$-strike receiver swaption $\leq$ a $K$-strike floor and this inequality is strict if the underlying fwd rates are uncorrelated, as shown by no-arb arguments going all the way back to Merton (1973).
The issue is that these markets trade separately for historical reasons - mainly because the two products serve different purposes for investor's rate hedge requirements. So that dishevels their intimate mathematical similarities.
The more relevant question is how much more the floor should be worth than the rec swaption? One can go about answering this in a couple of different ways ways:
- The academic/technical way is to analyze the short rate fwd/fwd (the state variable for pricing floors) correlation structure and, crucially, how these short rate fwds are related to the swap fwds (the state variable for pricing swaptions) - and ultimately contextualizing these correlations with the volatilities of each of these products... etc.
- On the other hand, the market/practitioner way is to just outright trade the floor/receiver wedges as a single product in its own right.
Note that 1. usually employs some form of historical analysis of the fwd rates leading to what can be thought of as "realized" fwd/fwd correlations, while 2. provides the corresponding "implied" correlations. A thorough understanding warrants both approaches.
Such correlation analyses/markets have far reaching consequences to understanding forward volatility markets (and hence Bermudan swaption valuation / optimal exercise criteria), mid-curve swaptions, LMM calibration techniques and hence rates exotics in general.
So what seems like a relatively simple question actually has quite deep implications.
A good (if somewhat dated) reference is The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence by Longstaff, Santa-Clara and Schwartz, J. Fin. 2001. Also see Stephen Blyth: An Introduction to Quantitative Finance, OUP (2014), Chapter 12.