The withdrawal of Jupiter from Turkey was much more valuable to the USSR in strategic terms; the PR optics of it were a secondary consideration. Additionally, the Kennedy-Khrushchev pact averted the risk of a US invasion of Cuba to topple the Castro regime, thus protecting the USSR's most important ally in the Americas. The Soviets calculated, begrudgingly, that if secrecy was the price of achieving those two strategic goals, that was a price worth paying. Getting Jupiter out of Turkey would involve Kennedy managing delicate relationships with Turkey, the wider NATO alliance and his domestic constituents — which would be much easier behind closed doors.
The Soviets regarded Jupiters in Turkey as a direct threat in much the same way that the US viewed the prospect of SS-4s and R-14s on launchpads in Cuba: it was just too close for comfort. It was a loaded gun pointed directly at the USSR's heart. For context: the PGM-19 Jupiter had a maximum operational range of around 1,500 miles. Launch points near İzmir, Turkey put them in effective range of the home base of the Soviets' Black Sea Fleet at Sevastopol (540 miles away), Kiev (850 miles), Minsk (1,080 miles), Moscow (1,300 miles), St. Petersburg (1,500 miles) — essentially all of the USSR west of the Urals, where most of the major population centres were to be found.
Consider that in 1962, intercontinental ballistic missiles (ICBMs) were still a new development: bombs deployed from long-range bombers and medium/intermediate-range ballistic missiles were the workhorses of both powers' nuclear arsenals. Both the US and USSR were still developing the capability to launch a strategic nuclear strike from home bases: the United States' first ICBM, the SM-65 Atlas, entered service in 1959; the comparable Soviet R-7A Semyorka was first deployed in 1960. Simultaneously, submarine-launched ballistic missiles were also just entering the arena: the UGM-27 Polaris, the US Navy's first SLBM, which had an operational range of 2,500 miles, entered service in 1961.
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