Compared to Germany, were great Britain and France better prepared for war in 1939 than in 1938?

The Battle Of France says "Non!"

Simply defining an objective measure of "war preparation" which can work between two countries using different equipment and tactics is quite difficult and would be its own question. Using quantitative means, like supply levels, or numbers of aircraft and tanks, ignores the qualitative differences between the equipment. It also ignores the radical change in tactics and pace of warfare which the Allies were about to be smacked in the face with.

And that's the ultimate analysis of a military, how did it do on the battlefield? How did Britain and France do on the ground against the Germans in 1940? Pretty damn poorly. Looking at why the Allies did so poorly highlights the problems of determining military readiness for armies which haven't been in a major battle for a generation.

Sometimes a battlefield loss can be up to tactical circumstances, but the Battle Of France is an entire campaign for the existence of a country. And it was a pretty clear German victory strategically and tactically. You have to make radical changes to the Allied concept of war to let the Allies win.

On paper, the Allies should have done all right. They were fighting a defensive battle from entrenched positions meaning they could expect to win with less. They had parity in troops, twice the number of artillery pieces, and over 1000 more tanks (and arguably better). The only quantitative material advantage the Germans had was in aircraft, nearly double the number. Aircraft provide flexibility of recon and firepower, more important to an attacker than a defender.

Prepared For The Last War

The Allies were well prepared for World War I, slow moving, grinding trench warfare. Their equipment, tactics, logistics, and generalship were all geared around establishing and holding a solid line and keeping it supplied with men and material. So in that sense they were very prepared for war... the last one.

Meanwhile, the Germans were busy changing the pace of warfare and making the Allied preparations moot. Many potential breakthroughs of WWI fizzled not because of enemy response, but because the troops breaking through didn't know what to do next; they sort of milled around waiting for orders. The Germans busied themselves reorganizing their entire chain of command to be flexible to changing circumstances expanding on the Stormtrooper tactics introduced in WWI.

They installed radios and other mobile communication equipment in their vehicles. They used light machine guns at the small unit level for offense, not just defense. Their air force coordinated with the ground force to provide close tactical air support and act as flying artillery to support offensive operations. They trained their commanders to bypass strong points rather than slowly bludgeon them.

In short, the German army was focused on probing the enemy for weaknesses, making a breakthrough, and then rapidly exploiting it before the enemy can respond to plug the gap.

The Allies were not prepared for this war, and found themselves always outflanked. Their communications and intelligence could not deliver a clear picture of the battlefield to their commanders fast enough, so orders were based on outdated or fragmentary information. Orders could not be issued to units fast enough, so units acted on old information. When they could stand and fight the Allies did quite well as at Arras and holding the line at Dunkirk, but those were the exception.

That is not to say the Germans were prepared. They took a huge gamble on new tactics and equipment, and hoped the Allies would not realize their gaping deficiencies. But they had a dress rehearsal, the Battle of Poland. Here they got to test out their new tactics and equipment, and as Military History Visualized shows in Panzers In Poland: Success, Failures & Losses, they found many problems.

Fortunately for Germany, the Allies gave them half a year to rectify them and recover their losses. The Allied hesitancy to take advantage of the bulk of the German army fighting in Poland speaks volumes to their lack of being prepared to fight this war. Had the Allies been more aggressive, they'd have found a very lightly defended German border, and history might have been very different. Instead, they stayed in their defenses and waited.

Had the Battle of France turned into a drawn out slugging match, German logistical and equipment inferiorities would have become a problem. This is illustrated starkly by the war on the East against the Soviets; it began as a wildly successful lightning war, but their failure to achieve decisive victory meant it turned into a slugging match the Germans could not win. Who was better prepared for that war? Hard to say.