Are \$\frac{1}{4}\$watt 4x\$\Omega\$ Resistor and \$\frac{1}{2}\$watt x\$\Omega\$ Resistor equivalent?
Resistors in parallel dissipate proportional amounts of the total power from each depending on the proportion of the current that is flowing through them.

Two equal resistors in parallel will share the current equally.  Ergo, they will dissipate half the total power each.

So yes, two equal resistors of twice the value and half the power in parallel will handle the same power as the original resistor.

To reiterate the maths differently:

Original = 1W, 50Ω. Current would be \$\sqrt{1/50}\$ = 0.141A.

100Ω resistor with half the current flowing would be \$(0.141/2)^2) \times 100\$ = 0.5W.