The lambda calculus is a far more beautiful theory of computation than Turing Machines.
That's a very subjective statement. I don't particularly like the fact that lambda calculus involves giving variables arbitrary names. I much prefer combinatory logic to lambda calculus, which only has two primitive symbols {S = ^xyz.xz(yz), K = ^xy.x}. There are other two-combinator bases as well, where the complexity is distributed differently. Taking this to the extreme, where one of the combinators is the identity function, we have {P = ^vwxyz.wx(wzy), I = ^x.x}.
It's an historical accident that the theory of computation is centered around TM's than lambda's.
Or a matter of practicality? I don't see how one could easily build a physical machine to directly run lambda calculus, whereas a Turing machine is very mechanical in its definition. Sincerely, Adam P. Goucher