Would the Germans have done better had they not gotten sucked into the Norway mess? Talk about a Pyrrhic victory, the won but in addition to their navy and air force taking heavy casualties, they lost a lot of quality infantry and from what I understand a disproportionate number of good officers.
Plus the paratroopers taking such heavy casualties pretty much turned Hitler off to that sort of operation in the future. I know the original plan called for para-drops into the Netherlands and Belgium but the debacle in Norway killed that idea. They probably wouldn't have made that much of a difference but who knows?
What really hurt the Germans in Norway was the Norwegians using National Radio to call up its army and the King urging his people to resist
This caused the German plan to be rushed and we end up with several units starting the attack early and others late.
The resulting casualties to their Paratroopers was bad but the sheer number of JU52's that where lost in the attacks. the Pilots of those aircraft were largely training instructors - so apart from the loss of airlift capacity it also heavily impacted the Luftwaffe's ability to train pilots which in part contributed to the eventual Entente Air Superiority.
Lack of paratroopers also impacted the Dutch campaign with Dutch forces denying the German Army use of several key bridges early on any buying the Dutch army time to redeploy.
And then there is the loss to the German Navy!!!
3 heavy and 2 light Cruisers lost + 2 light Cruisers damaged (mostly to the Norwegian fortresses)
15 Destroyers destroyed or declared total losses and worst of all Scharnhorst and Gneisenau getting badly damaged by Renown on the 9th April with Gneisenau being declared a total loss* and Scharnhorst taking 6 months before she could sortie again.
With only U Boats to threaten the Atlantic convoys this pretty much freed up the Home fleet for other duties and with Italy not getting involved more British and French DDs could be freed up for Convoy duties.
And when Salazar allowed British bases in the Azores in late 41 the ability to cover convoys with Maritime patrol aircraft increased dramatically.
*Her C Turret was used to replace Scharnhorst's destroyed B Turret and while some work was started on repairing Gneisenau in late 41 and there was a plan to refit her with 3 twin 15" guns, the war ended before work could start.